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Spectral estimates for high-frequency sampled continuous-time autoregressive moving average processes. (English) Zbl 1282.62192

Summary: In this article, we consider a continuous-time autoregressive moving average (CARMA) process driven by either a symmetric \(\alpha\)-stable Lévy process with \(\alpha \in (0,2)\) or a symmetric Lévy process with finite second moments. In the asymptotic framework of high-frequency data within a long time interval, we establish a consistent estimate for the normalized power transfer function by applying a smoothing filter to the periodogram of the CARMA process. We use this result to propose an estimator for the parameters of the CARMA process and exemplify the estimation procedure by a simulation study.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M15 Inference from stochastic processes and spectral analysis
62M09 Non-Markovian processes: estimation
60G51 Processes with independent increments; Lévy processes

Software:

AMPL; MINOS
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References:

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